How in the world do we balance reactions? And what does that even mean?

First, we need to know about the Law of Conservation of mass. The law of conservation of Mass states that matter cannot be created or destroyed; only changed. What that means is, the number of moles for each atom on the reacting side must equal the number of moles for each atom on the product side.

In this picture, let's say we're looking at this one, we have FeCl3. This is basically a written out reaction. So we're saying Iron comes along and reacts with Chlorine. It produces something new called Iron (III) Chloride5. So we want to make sure we balance the equation that we know that we have the proper ratios, proper amounts of each substance.

So we can't change the substance themselves, meaning we can't do anything with these subscripts. But we can change the amount of that. So we'll put a line here showing. We can put numbers if you have the amount of substance changed.

So easy way to go by doing this, is to write down all the atoms reacting on the reactant side, and all of the products reacting on the product side, or formed n the product side. So we have Fe, and we have Cl. In the product side, I'm just going to write it the same order; Fe and Cl and FeCl3.

I count; I have one Fe atom, and two Cl atoms. This side I have one Fe, and 3 Cl. I want these numbers to be the same on both sides. According to law of conservation of mass, they must be the same. So right now I have the correct number of ion, and atoms on both sides. You have 1, and 1, my point needs to change. I have two on the reacting side, and three on the product side. So how am I going to get these numbers to be equal?

If I multiply this by 3, and multiply this by 2, I get 6, which means I have to do that in front of here. So I multiply this by 3, and I take that is 3 times 2 is 6. ISo it's 3Cl2 atoms or molecules which means I have 6Cl atoms. I multiply this by 2, 2 times 3 is 6. I have 6 Chlorine atoms, quite atoms.

That means I just changed the Fe. That means I have instead of 1, now I have 2. Which means I can put 2 in front of here to make them the same. So this is what we call a balanced reaction. Also notice, the coefficients, these big numbers, their lowest ratio. If it was ended up being 4, 6, 4 you'd want to reduce it 2, 3, to the lowest ratio. Notice there are fractions. Typically you do not deal with fractions as your coefficients. You might when dealing with other types of reactions, but in your case right now, you do not deal with any fractional coefficients.

Let's look at something a little bit more complicated. First, let's identify what type of reaction this is. Iron plus Chloride is Iron(III)Chloride. This is a synthesis. I know that, because that is one product. This has two compounds, and they're switching partners. This I'm going to say is double replacement.

In a double replacement reaction, notice the polyatomic ions stay together. So when I actually count my atoms up, I have Calcium on this side, I'm going to keep my Hydroxide together, because notice Hydroxide are actually going to make this HoH. That might make it better for you. HoH is another way of saying water, but it also shows us that it has a Hydroxide ion in it. So I can keep that there. I can count it together.

Then I have a Hydrogen, then I have a Phosphate. The same thing here. I want to put it all in the same order, so it's easy for me to compare. I'm going to count everything. I have 1 Calcium, 2 Hydroxides, 3 Hydrogens, and I Phosphorous. I have 3 Calciums, 1 Hydroxide, 1 Hydrogen, and 2 Phosphates.

Let's start from the beginning. How am I going to make this a 3? This 1 a 3? I'm going to multiply. Notice, I can only put coefficients on these lines. I'm going to put a 3 here. What that does is changes this to a 3, but it also changes the Hydroxides. Each atom I have two of them. So if I have three atoms, I have 6 of them.

So now I want to change the Hydroxides on the product side. I want to make this a 6, because that would change this to 6. That would also change my Hydrogens to 6. Notice I'm separating them out from OH, and H.

On the reactant side, I only have 3 Hydrogens, but I have 6 in the product. So I'm going to put a 2 in front. That means I have 6 Hydrogens, and 2 Phosphates. In the product side, I have 2 phosphates, so everything is equal. If it doesn't have anything there, I could put a 1, but most of the time you're not going to see that 1. It is basically a 1 there. This is my lowest ratio, and so this is a balanced reaction.